# complex vectors and matrices

(30 minutes to learn)

## Summary

We can define complex vectors and matrices with properties closely analogous to their real-valued analogues. Complex matrices come up when dealing with eigendecompositions of non-symmetric matrices. They are also used in computing the fast Fourier transform.

## Context

This concept has the prerequisites:

- complex numbers
- dot product (The Hermitian operator is used to define the complex analogue of the dot product.)
- matrix transpose (The Hermitian operator is the complex analogue of the matrix transpose.)

## Goals

- Know the definitions of the Hermitian operator and the complex dot product

- Why is the Hermitian operator used for complex matrices rather than the matrix transpose?

## Core resources (read/watch one of the following)

## -Free-

→ MIT Open Courseware: Linear Algebra (2011)

Videos for an introductory linear algebra course focusing on numerical methods.

## -Paid-

→ Introduction to Linear Algebra

An introductory linear algebra textbook with an emphasis on numerical methods.

Location:
Section 10.2, "Hermitian and unitary matrices," up to "Hermitian matrices," pages 501-502

## See also

-No Additional Notes-